Punch—a blend of sugar, spirits, spices, water and citrus, usually served in a large bowl for sharing—didn’t used to be served at places like Jigger & Pony, where waist-coated mixologists take pride in cocktails crafted with house-made syrups and hand-carved ice. But from Brooklyn to Bangkok, the drink is making an appearance in craft bars around the world.

Experts believe that punch, traditionally made with five ingredients, can be traced back to Asia, specifically 17th-century India. Some say its name sounds like panca (Sanskrit for “five”).

David Wondrich, the author of “Punch: The Delights (and Dangers) of the Flowing Bowl,” says there’s “no iron-clad proof,” but a common theory holds that British merchants and sailors in the early East Indian trade made the drink from “little casks of spirits” left over from their travels.

A few centuries later, punch retained its slapdash connotations. According to Joe Alessandroni, general manager at Singapore bar 28 Hong Kong Street, just a decade ago it was considered “something you drink at a frat party or at a tacky bar that gives you a headache afterward.”

But today, punch is finding its way onto the menus of Asia’s hippest drinking establishments. And in contrast to the sloppy, fruity concoction ladled out at barbecues or spiked at high-school proms, punch these days is looking—and tasting—decidedly sophisticated.

At 28 Hong Kong Street, patrons can order a punch made with lemon and boiling milk that traces its origins to a recipe from America’s Deep South. Over in Melbourne’s Eau De Vie, the best-selling vodka-based punch is boosted with raspberry oolong and Russian caravan tea then topped off with liquid nitrogen.

Proper punch is time-consuming to make. To start with, extracting oil from lemon peels, as required for classic punches, involves leaving them in a mason jar with sugar overnight. It’s also complicated by the large quantities of ingredients required, and the lack of storage space in bars, which limits the amount of punch they can make. 28 Hong Kong Street, for instance, will only make four batches at a time, according to Mr. Alessandroni.

What draws bar patrons to punch? For one thing, scooping a cocktail out of a punch bowl provides a fun factor. “It’s more enjoyable for people to sit down and share the same drink,” noted Mr. Almenning. “If you order a margarita, all you do is drink it.”

The drink does provide at least one obvious benefit to bartenders: A single bowl, which often contains more than a dozen serves, can satisfy a group of customers for hours. “The production of the drink takes forever, but on the night you can serve it up quick,” said Sven Almenning, Eau De Vie’s director.

For customers, it doesn’t come cheap. Fabien Marcault, manager of tiki-themed bar Honi Honi in Hong Kong, said that his Around the World punch—made with several rums and liqueurs, vanilla syrup and tropical fruit juices—is the costliest cocktail in the city, at 2,888 Hong Kong dollars (roughly US$370) a pop. At Jigger & Pony, punches like the citrus-based Chatham Artillery, topped off with a bottle of sparkling wine, go for 210 Singapore dollars (US$165) a bowl.

Punch also offers the element of spectacle, with some watering holes presenting their punches in quirky utensils such as crystal bowls, vintage-styled globes and old-school metal flasks. Eau De Vie’s Versailles Experience—a pale-yellow medley of gin, absinthe and juices—arrives in a four-spout fountain balanced on a base shaped like a reclining woman. There is often a waiting list since the bar has only three fountains, which “cost $400 a pop,” Mr. Almenning said.

According to Colin Chia, an Asia-Pacific manager at spirits maker Diageo, punch is now such a fixture “in matured cocktail markets like Australia and Singapore” that the company’s World Class bartending competition this year dedicated a round just to punch-making techniques. (While some bars use “punch” for any drink large enough to serve to groups, to classify as a true punch it should have at least four of the original five ingredients.)

With punch’s growing popularity, bartenders are beginning to adapt. Cocktail punches typically have an alcohol content by volume of about 15%, but given that they are typically served with up to 1.6 liters in a bowl, some establishments are reluctant to offer them to smaller groups.

Punches in smaller portions are already on the menu at 28 Hong Kong Street, and the head barman at Jigger & Pony, Aki Eguchi, said he is considering presenting punches in single serves.

For now, however, “this is not something I might order when out alone with my girlfriend,” Mr. Eguchi said.